A fixed parameter algorithm for the minimum number convex partition problem

Authors:
Magdalene Grantson;Christos Levcopoulos
Affiliations:
Department of Computer Science, Lund University, Lund, Sweden;Department of Computer Science, Lund University, Lund, Sweden
Venue:
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Year:
2004

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Abstract

Given an input consisting of an n-vertex convex polygon with k hole vertices or an n-vertex planar straight line graph (PSLG) with k holes and/or reflex vertices inside the convex hull, the parameterized minimum number convex partition (MNCP) problem asks for a partition into a minimum number of convex pieces. We give a fixed-parameter tractable algorithm for this problem that runs in the following time complexities: – linear time if k is constant, – time polynomial in n if $k=O(\frac{{\rm log}n}{{\rm log log}n})$, or, to be exact, in O(nk$^{\rm 6{\it k}-5}$ 216k) time.